Determinants of matrices related to the Pascal triangle
The aim of this paper is to study determinants of matrices related to the Pascal triangle.
Determinants of multiplicative Toeplitz matrices
Détermination des diviseurs à coefficients commensurables, d’un degré donné, d’un polynôme entier en à coefficients commensurables
Determining Integer-Valued Polynomials From Their Image
This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on .
Die Primfaktorzerlegung der Werte der Kreisteilungspolynome.
Die Primfaktorzerlegung der Werte der Kreisteilungsprobleme. II.
Distribution of primes and a weighted energy problem.
Distributional properties of powers of matrices
We apply the larger sieve to bound the number of matrices not having large order when reduced modulo the primes in an interval. Our motivation is the relation with linear recursive congruential generators. Basically our results establish that the probability of finding a matrix with large order modulo many primes drops drastically when a certain threshold involving the number of primes and the order is exceeded. We also study, for a given prime and a matrix, the existence of nearby non-similar...
Divisibilité des polynômes relativement aux puissances d'un nombre entier
Divisibility of integer polynomials and tilings of the integers
Divisibility properties of generalized Vandermonde determinants
Divisibility properties of Smith matrices
Dvě poučky o kuželosečkách
Easier Waring problems for commutative rings
Effective finiteness theorems for polynomials with given discriminant and integral elements with given discriminant over finitely domains.
Effective Nullstellensatz for arbitrary ideals
Let be polynomials in variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials such that . The effective versions of this result bound the degrees of the in terms of the degrees of the . The aim of this paper is to generalize this to the case when the are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
Ein Cyclus von Determinanten-Gleichungen. (Eine analytische Erweiterung des Pascalschen Theorems).
Ein Determinantensatz.
Elliptic curves with bounded ranks in function field towers
Équations diophantiennes polynomiales à hautes multiplicités
On montre comment écrire de grandes familles, avec de hautes multiplicités, de cas d’égalité pour l’inégalité de Stothers-Mason (si sont des polynômes premiers entre eux, le nombre exact de racines du produit dépasse de le plus grand des degrés des composantes . On développera pour cela des techniques polynomiales itératives inspirées des décompositions de Dunford-Schwartz et de fonctions de Belyi. Des exemples d’application avec les conjectures ou de M. Hall sont développés.